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Nonlinear waves in compacting media. (English) Zbl 0587.76165
An investigation of the mathematical model of a compacting medium proposed by D. P. McKenzie [J. Petrol. 25, 713-765 (1984)] for the purpose of understanding the migration and segregation of melts in the Earth is presented. The numerical observation that the governing equations admit solutions in the form of nonlinear one-dimensional waves of permanent shape is confirmed analytically. The properties of these solitary waves are presented, namely phase speed as a function of melt content, nonlinear interaction and conservation quantities. The information at hand suggests that these waves are not solitons.

MSC:
76S05 Flows in porous media; filtration; seepage
76B25 Solitary waves for incompressible inviscid fluids
86A15 Seismology (including tsunami modeling), earthquakes
76M99 Basic methods in fluid mechanics
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[1] Drew, Stud. Appl. Math. 50 pp 205– (1971) · Zbl 0225.76051 · doi:10.1002/sapm1971503205
[2] Benjamin, Phil. Trans. R. Soc. Lond. 272 pp 47– (1972)
[3] DOI: 10.1063/1.863011 · Zbl 0425.76019 · doi:10.1063/1.863011
[4] Walker, J. Geophys. Res. 83 pp 6004– (1978)
[5] Scott, Geophys. Res. Lett. 11 pp 1161– (1984)
[6] Richter, J. Geology 92 pp 729– (1984)
[7] DOI: 10.1130/0016-7606(1974)85 2.0.CO;2 · doi:10.1130/0016-7606(1974)85 · doi:2.0.CO;2
[8] Olver, Math. Proc. Camb. Phil. Soc. 85 pp 143– (1979)
[9] McKenzie, J. Petrol. 25 pp 713– (1984) · doi:10.1093/petrology/25.3.713
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